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Jack has a giant apple pie. On the first day, he eats half of the pie. For each following day, he eats half as much pie as he did the day before. What fraction of the original pie did he eat on the tenth day?

Question

Jack has a giant apple pie. On the first day, he eats half of the pie. For each following day, he eats half as much pie as he did the day before. What fraction of the original pie did he eat on the tenth day?

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Solution

On the first day, Jack eats 1/2 of the pie.

On the second day, he eats half as much as the first day, which is 1/2 * 1/2 = 1/4 of the pie.

This pattern continues for each following day.

So, on the tenth day, he eats 1/2^10 of the original pie.

Therefore, the fraction of the original pie that Jack eats on the tenth day is 1/1024.

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